In another thread C. Curtius Philo Aurelianus asked an important question: "What is the difference between quantitative and qualitative logical questions?" What he meant is questions that cannot that easily be quantified, so that we can use deductive reasoning to come to a clear conclusion, but questions like: "What is better socialism or capitalism?" or "Should I carry an umbrella today?"

It is obvious that we cannot use deductive reasoning for these question, because we have no premises, no general principles to deduct from.If we were able to establish a general principle like "The means of productions should be public and not private." then we could be able to answer the first of the questions above by deductive reasoning. From this premise and the definition of socialism as a system where the means of productions are public, we can conclude that socialism is better. But if our premises are that private property should not be restricted and that only capitalism protects private property, we will conclude that capitalism is better. Both deductions are logically valid, but different premises lead to different conclusions.

There are very few general principles that are true a priori, i.e. before empirical experience. An example would be mathematical rules. But most general principles have to be established a posteriori, i.e. after empirical observation. They depend on the world and the laws of nature.And here we can already see, what we are dealing with, when it comes to inductive reasoning - science or natural philosophy.

Inductive reasoning establishes the general principles from particular observations in the world. Then deductive reasoning is able to make conclusions and predictions based on these general principles.. If these predictions are confirmed, they strengthen the principles; if they are not confirmed, the general principle has been disproved. Both, inductive and deductive logic work together in some kind of hermeneutic circle:

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Inductive reasoning is probabilistic. This means it only states that, based on the examination of a finite number of specific cases, the conclusion (the resulting general principle) is probable. It remains uncertain whether the established general propositions are universal or have so far unknown exceptions or describe only a subset of a more general principle.

The probability of inductive reasoning is based on either strong or weak premises. Strong premises with high probability result in cogent conclusions. Weak premises based on only a few instances lead to faulty generalizations, which are inductive fallacies.

Among the classic philosophers there was no better expert on inductive logic than Epicurus. It is often assumed that Epicurus rejected the strict application of logic in his philosophy, but this is not true. Epicurus questioned the validity of deductive reasoning, if it was not based on empiric observation. He did not question the validity of logic itself, but his logic was inductive. He developed the scientific method long before Galileo Galilei or Newton. And his method was so successful that he was able to confirm Democritus' atomic theory and refined it with the uncertainty principle that was later in the 20th century confirmed by Heisenberg and is a central part of quantum mechanics. He also proved the infinity of the world and the necessity of a maximum speed of causality in the universe, which Einstein later identified as the speed of light. Long before Darwin he concluded that life on Earth must have evolved from dead matter and not from divine creation.Epicurus' method was based on the following rule:Nothing should be believed, except that which was tested through direct observation and logical deduction.He also understood that inductive reasoning was not about finding the ultimate truth, but was utilitarian, this means science would be without purpose, if it does not help us to obtain ataraxia by making our lives easier or freeing us from irrational worries due to our ignorance (PD11). In this regard he was ahead of modern science who believes in the collection of useless knowledge about things that do not affect us (e.g. black holes, exoplanets beyond our reach).From this utilitarian approach we should be aware that any theories developed from inductive reasoning that are able to explain all known observations and make correct predictions are equally valid. It is pointless to discuss, which of them is "true". General propositions based on inductive reasoning do not claim to be ultimate truths, but derive their value from their utility and their ability to make probable predictions.

From a philosophical point of view there would be no need to write more about inductive reasoning, because I would simply describe the scientific method and there are already enough books available about this topic.However I would like to point out some central principles.

FalsifiabilityOne of the characteristics of the scientific method is that all general principles and theories derived from inductive reasoning must be falsifiable. The philosopher Karl Popper defined falsifiability as the demarcation criterion of science. If a thesis is unfalsifiable and therefore untestable, it is unscientific.

Causality

Almost all of science is about discovering the mechanisms of causality. The English philosopher John Stuart Mill established the following tests of causality.

a must cause Z, because:

Method of AgreementWhenever Z is seen, a is also found.

Method of DifferenceIf a is removed, Z goes away.

Method of Concomitant VariationsIf a is changed, Z changes correspondingly.

Method of ResiduesIf the dominating effect of b on Z is removed, the residual Z variations correlate with a.

Inductive Fallacies

The rules of inductive reasoning are necessarily less stringent than the rules of deductive reasoning. They do not provide absolute proof but seek to provide strong evidence for a conclusion. Inductive conclusions can never be certain, only highly probable.Faulty methods of reasoning that do not contribute to a strengthening of a conclusion are considered inductive fallacies. The following list describes the most common inductive fallacies, this means they are common systematic errors in inductive reasoning. It is not uncommon to find these fallacies even in modern scientific primary research.

Argumentum ad Ignorantiam (argument from ignorance) – The assumption that a lack of evidence to the contrary is an evidence in itself. Thereby the burden of proof (onus probandi) is shifted to the refutation of the claim.

Argumentum ad Temperantiam (false compromise) – The assumption that the compromise between two positions is always correct.

Association Fallacy – The assumption that two things sharing a property are both true/false.

Attribution to Accident – Ignoring an exception to a generalization.

Base Rate Neglect – Ignoring prior probabilities (base rate) of a necessary condition for an evidence by only taking into account the probability of the evidence instead of the total probability.

Causal Oversimplification – Assumption that there is one, simple cause of an outcome when in reality it may have been caused by a number of only jointly sufficient causes.

Circulus in Probando (circular reasoning) – Beginning an argument with what is attempted to prove. So the conclusion is its own premise (petitio principii). One example of circular reasoning is a question that presupposes something that has not been proven or accepted and limits the possible answers to an affirmation of the presupposition (plurium interrogationum).

Continuum Fallacy – Improperly rejecting a distinction because of a continuity of states between them.

Cum Hoc, Ergo Propter Hoc (correlation proves causation) – Assumption that correlation between two variables is a sufficient evidence that one causes the other. (see above - Mill's tests of Causality are necessary, not sufficient conditions of causality.)

Fallacy of Composition – The assumption that something true of part of a whole must also be true of the whole.

Fallacy of Division – The assumption that something true of a thing must also be true of its parts.

False Analogy - An argument by analogy in which the analogy is poorly suited.

False Dichotomy (black-or-white fallacy) – The assumption that two alternative statements are the only possible options, when in reality there are more.

Faulty Generalization – Conclusion that is based on only one or a few instances.

Gambler's Fallacy – The incorrect belief that separate, independent events can affect the likelihood of another random event. (A series of even numbers drawn in a lottery or roulette do not make it more likely that an odd number will follow next.)

Mind Projection Fallacy – Assuming the own way to think is how others think and act..

Nirvana Fallacy – Rejecting solutions to problems because they are not perfect.

Regression Fallacy – Ascribing a cause where none exists while failing to account for natural fluctuations.

Reification (hypostatization) – Treating an abstraction as if it was a concrete entity.

Retrospective Determinism – The argument that because some event has occurred, its occurrence must have been inevitable beforehand.

Reversed Direction – Reversing cause and effect.

Suppressed Evidence (cherry picking) – Pointing at individual cases or data that seem to confirm a particular position, while ignoring a significant portion of related cases or data that may contradict that position.

Wishful Thinking - Making an assumption because it is pleasing to imagine, rather than according to evidence or reason.

As we have seen, inductive logic is not as rigorous and absolute as deductive logic. Still we know from science that there are clear rules about valid methodology and there exists a consensus in the scientific community. It is very well possible to quantify the world that surrounds us. The scientific method provides us with the tools to use reason and logic when dealing with empiric phenomena. There is nothing in the world, which escapes inductive reasoning.

The Skeptics have often argued that nothing is certain. But such a view is based on intellectual laziness. Even if nothing is certain, we are quite well able to tell what is probable.Socrates is quoted as saying: "I know that I know nothing."I would answer him: "We know all that we need to know."Because if something affects us, then we have plenty of information at our disposal to form our theories about it.If something affects us only a little, then we have little information to form a theory, but it is also of little concern to us.If something does not affect us at all, then we have no information about it to form any theory, but it is also of no concern to us.

This concludes the series of threads about the principles of logic.We have heard about the axioms of classical logic, about two approaches to deductive logic (syllogistic logic and propositional logic) and in this thread about inductive logic and the scientific theory. We have seen that there are universally accepted rules of logic, about which we can reach a consensus with every reasonable being.What remains to discuss now is the application of these rules in our daily life. Because logic is not an abstract academic principle only of use for some philosophers, it can be a guideline for everyday problems in life that gives us always the optimal answer in every situation.